Now the bad news is that Apple has patched Evasi0n untethered jailbreak exploits and if you have accidentally updated to iOS 6.1.3 firmware then you have lost your untether-jailbreak on your idevice and Evasi0n jailbreak tool is not yet updated to support iOS 6.1.3 firmware. The good news for users who have A4 iPhone and iPod touch, they can still get tether jailbreak on iOS 6.1.3 firmware.

Step 1:Now download Redsn0w on your PC and open it up. Windows users should open RedSn0w in Administrator mode. Click on jailbreak option in Redsn0w Window.Step 2: Now put your iPhone, iPod touch or iPad in DFU by following on-screen instructions:
To enter DFU mode:

Hold Power and Home buttons for 10 seconds
Now release the Power button but continue holding the Home button for 10 more seconds
You device should now be in DFU mode (black screen)

Step 3: Click on the Extras button and then on the select IPSW button and select iOs 6.1 IPSW downloaded above. After pointing the IPSW files click on Jailbreak on Redsn0w and it will start the kernel patching process.

Step 4: After completing some process a new window will open and check install Cydia option and click on Next.

Step 5: Now Redsn0w will start jailbreak process on your iDevices running iOS 6.1.3 firmware and you just have to wait for the completion of jailbreak process.

As we mentioned this before that this jailbreak is tethered and you need to launch Redsn0w, select “Extras”, then”Just Boot” in order to boot your device tethered.